With Classic 93, the bypass was over quickly and box marking completed the 9’s. Then three lines in, a hidden single starts a rapid collapse. Along the way, you see a chain of identical bv 38 develop and collapse before reaching remote pair length.

Here is the grid, just after the naked single and hidden single, and just as the collapse is starting. Following a collapse, like box marking and line marketing, is a routine activity. But it is also satisfying, like knitting and whittling. The trace looks complicated to the uninitiated. But it builds itself, with simple, efficient steps.

On Classic 120, we have only the bypass to report. The trace spreads across the page, before dropping in the collapse, leaving many causes unused.

For Advanced only readers, Forest’s Classic 144 is worth waiting for. It requires a parade of boomerangs, and has a surprising Sysudoku finish.

After that, the Classic review finishes in Basic, along with reports updating another review . If you have a needed update in mind, let me know in a comment.

]]>The bypass threatens to take over, but leaves an XY playground.

The line marked grid gives all of the Sysudoku Basic results.

Two fill strings of one value is a bit unusual.

The generous bv field predicts a productive XY railway system.

But first we look for UR, SdC, APE, and other methods not requiring maps and panels.

Here we have a classic indeed, an ALS toxic pair. The 3 value is contested, but 8r5c9 sees both groups of 8 that would be locked in by the winner.

Significantly, a 4-value Bent Almost Restricted n-Set, a BARN, can be superimposed around the ALS pair. Only the 8 values are bent. The removal is not as significant.

The significant removal is 6r1c4. It’s a 3-node XY-chain, adding an NEr1 boxline removal and a naked triple in c4.

Collapse is immediate.

Next is Classic 96 (left) and 120. Both are solved in Basic. Have your versions ready.

The Guide pages *Sysudoku Basic*, and *Begin With the Bypass* have been updated. If you’ve been putting off a serious evaluation, now is a good time.

Many placements are made in the bypass and in line marking, but with many unsatisfied 3-fills. Tracing it out, you can add 8-wing markers to prevent the addition of wing victims to the grid.

The grid with these markers reveals an imbalance of values , with 3, 6 and 8 predominating.

X-wings are spotted with routine checks in line marking, but finned X-wings show up on an X-panel. Analyzing for both as each X-panel is completed, this fish and X-chain are spotted at the same time.

In this case, the X-panel jumps ahead of the bv map, adding a central bv to this XY network. There just has to be a way to connect a remote pair chain of at least four, and there is.

It takes a little follow up to get to the remote pair.

Now we can lay on a healthy blue/green cluster and still throw a red/orange one over the 36 bv.

Common values show that

Not(red and green) => orange or blue.

In cell r5c6, this fact traps 3, allowing a slink to merge red and blue, along with orange and green.

In the merged cluster, the trap in r1c2 => NW4 => SW3 wraps blue, and the solution is full of little green men.

Next week, be ready with your Classic 72. James Forest wants you to get the most from his other 240 puzzles. You may have two bv scan rewards right out of the line marking gate.

]]>

The bypass fills the East boxes with 20 placements, including naked pairs and two immediately resolved 3-fills.

How many UR signposts are there among the naked pairs in this line marked grid?

Out of five naked pairs, three possible UR’s call for a closer look, for Type 2b.

The same bv are also covered in an unproductive scan for Sue de Coq.

The UR is there.

On the bv map, no ANL, but the single i471-wing defines a toxic set. No victims, but we can leave the toxic set markers on the grid copies, as we move on to the X-panels.

The 4-panel closes Classic 24 out with a finned swordfish. 4r6c1 is the fin, and the removal of 4r4c2 in the fin box brings in C4 and the collapse. It turns out that two of the toxic set members are true.

Next time, James Forest’s Classic 48 will carry us further along. Can you say just how far?

The Guide pages on the Unique Rectangle and AIC Building are updated.

]]>

After a generous bypass, KD Insane 4×5 starts with an overabundance of 1,8 and 9-candidates. If you haven’t looked at the updated post yet, find the Type 2b unique rectangle. There’s a floor to ceiling slink . The Solving Tools page has a UR chart.

Next, 4×5 goes directly to AIC building with a series of boomerangs that fit on one grid, because all but the first is an extension of another. The common infrastructure is an ALS that stays in the path as the solver keeps reaching back to an earlier and earlier starting point. Directions come with it, if you’re like me, assemble first and read later.

Sudokuwiki treats these as separate findings, each one enabling the last.

Unwilling to be left out, 4×5 had to provide Sudokuwiki an ALS boomerang ANL. The 8-group of the ALS is one terminal, and group member 8r1c7 is the other terminal. The 8-group has to contain a true 8.

This time, when Sydokuwiki gives up, it’s time to do the freeforms and lettering on four X-panels of Insane 4×5 for a Limited Pattern Overlay, covering X = 3, 4, 5, and 6, with 3, 3, 6, and 4 patterns respectively. Also included is the 7-panel with 2 patterns in a single 7-wing.

The idea is to discover any patterns eliminated, with corresponding candidate eliminations, due to conflicts between patterns. It takes organization, because a pattern is not eliminated unless it conflicts with every pattern of another value. To begin, we have to name every possible pattern of the participating values.

Now every cell of each pattern is examined for conflicts with other values, to be translated into conflicts with patterns of other values.

It’s a Big Data problem, the kind normally done by computer, barely kept humanly possible be restricting the data.

The 2013 post illustrates the conflict tables that keep the books as the scanning is done and gives the readout of eliminated patterns. It doesn’t quite work on 4×5, but it sometimes does. The process qualifies as a logical solution, as opposed to a trial.

In earlier Insanes, coloring trials were set up with apparent clusters made up of pairs of patterns, effectively testing two patterns at a time. Doing that on the 4-panel, with 3 patterns, the true pattern will eliminate a false pattern paired with it, so a contradiction eliminates both patterns.

One trial, on 4a and 4b reached a contradiction in a lengthy trial, leaving 4c to be installed as the true pattern. One color is wrapped in the follow up, and when it stalls, a remote pair and a lengthy XY-chain ANL collapse all resistance to the solution.

The updated review table, with which you can compare the Insane collection to others reviewed in Sysudoku, is in the post of 10/22/2013.

Next post will have parting comments on contributions of the Insanes to the Sysudoku Guide, and an introduction to the next collection review, Classic Sudoku, Book 30 by James Forest. The review starts with Classic 24 above, and includes every 24^{th} for the preselected 10 review puzzles. Have your version ready.

]]>

Here is the freeform that demonstrates how a dumbfounding announcement by Sudokuwiki can be humanly verified. It was that 5r9c9 is an orphan, i.e. it belongs to no 5-pattern. That hits anyone defeated by twisted jungles of freeforms where it hurts, especially when looking at such an X-panel. But then, when you see that the South box claims the only remaining r8 5, and SW must have the r7 5, you’re more prepared to look at how far this goes. And it’s not far.

The announcement orphaned 5r7c as well, so before looking at the 2013 post, you can freeform your way to that conclusion. We both can remember to check three line banks or towers to see what gets through.

Now in a puzzle saturated with 8’s Sudowiki demonstrates that a cloud of candidates can have weaknesses. Two ANL strung together eliminate two from a column of eight. One uses an ALS 8-group as a slink chain terminal.

Then we get the second ALS boomerang ANL in this series. An ALS 8-group and a candidate member are terminals of the slink chain, confirming the group contains a true candidate.

Then when Sudokuwiki retires to a neutral corner to catch a breath, I pile on with a pink olive move very similar to the 5 orphan eliminations above.

Here are the 8-candidates that are left. The two members of the ALS 8-group are involved in a pink olive slicing that is smothered in candidates. However there are only three patterns that follow the pink slice established in the first three lines. In a trial of these three patterns, 13 orphan 8-candidates are removed, and new clues and bv are created by the removals. That means the likelihood of a solution or a contradiction is very high. Either one is a large advance. A contradiction would remove at least the three pink candidates and create at least six clues. Both of these prior facts are evident in the grid as the trial begins.

In the trace to the solution, you can see where the continuing collapse is dependent on one clue. And as you step through the trial, you can see the near ambiguities that make Insane puzzles so hard.

Next report is on the update of KrazyDad Insane volume 4, book 10, number 5. Sorry about bypassing the LPO examples in 495, but 4×5 fills in for a process demonstration. There are other places where it is more needed, and more decisive.

]]>Here is the 9-panel when KD 485’s ALS boomer discovers that 9r2c2 and 9r2c9 are a toxic set. It looks unpromising, until you take the toxic set into account. Do that for yourself, then enjoy the parade of Sudokuwiki moves in the updated post. There’s a BARN, an unaligned APE, and classic 263-wing.

A particularly impressive move is this ALS aided confirming ANL promoting 9r5c4. For you or me, it could have started as a possible boomerang, leaving 9r5c4 in search of a wink back into 1 to eliminate that 1. But since the cell is a bv, it also puts two slinks around 9. Actually it’s the same result, whether you list it as a confirming or eliminating ANL. With another candidate in the starting cell, it would be only eliminating.

When the solver invokes coloring for a single trap on 3r4c3, we expand the cluster as far as it will go, in pursuit of a possible wrap. The 363-wing and Wr6 boxline elimination are reported on the same grid. The wrap is not long in coming.

The next update report is on KD Insane 495, already up.

]]>As if the puzzle were aware that KD 475 was solved by SASdC trial, 485 starts with a cautionary example on how to set up a Single Alternate Sue de Coq trial with the second alternate represented by a bv in the SdC intersection. The trial is deferred for a last resort, and is never needed.

Then after one X-chain ANL, Sudokuwiki offers a series of six AIC building ANL, the last three on the very same set of links.

This last structure is an extraordinary AIC ANL. One terminal of the slink chain is a value group in an ALS. The other is a candidate member of that group. In effect, the ANL proves that the 9-group is a toxic set, with three victim onlookers.

Two writers with two different purposes in mind are called upon to account for it. Andrew Stuart, who built Sudokuwiki and wrote its code, classifies the ANL above as a *digit forcing chain*. The updated post on Insane 485 explains why this labeling is no help to the human solver.

The description above covers *what it is*, but that isn’t enough. I didn’t find this thing. My job is to account also for how a human could find it, or recognize it when it occurs by accident. The distinguishing feature for spotting has to be the ALS value group with one candidate member slinking out of the ALS. If the AIC beginning this way gets to a candidate that sees another value group of the starting ALS, the value group is a toxic set. A name reflective of all this is *the ALS boomerang*.

The solver continues with good examples of a Type 2b unique rectangle, a naked triple, two esoteric boomerangs and a rare form of ALS toxic set, but eventually gives up.

A pink olive analysis of the 2-panel uncovers two disjoint pairs of freeforms for cluster trials.

Dashed pink and solid olive are paired, then solid pink and dashed olive, to give two complete pattern clusters.

Each cluster is added to a small blue green cluster for a separate trial. In the trial of the solid pink and dashed olive cluster, the latter is quickly wrapped. In this example of graphic confirmation, orange removes all 6 candidates from r4.

Next time I report an updated second chance solution by Stuart’s Sudokuwiki solver, when given the ALS boomerang’s clue by a very rare and very human pattern analysis.

]]>After two almost nice loops which Sysudoku identifies for spotting purposes as boomerangs, I’m inclined to name another new form of ANL, again an aid to spotting. One terminal of the ANL is an ALS with a single candidate value removed by an incoming wink. The victim sees the resulting naked pair. To call attention generally to this kind of AIC node, I call it a *subset node*. The strong link is between ALS value groups in the subset.

The corresponding Sudokuwiki message carries no spotting insight. That is the first concern, that the message reflects the solving code of the solver, but not the filtering necessary for practical human solving.

A second concern is that in the Sudokuwiki explanation of this example. It is treated as a loop around 2r8c1 such that wherever you start, the AIC in each direction forces 2r8c1 to be false. The two directions are obtained by choosing a digit on the loop and assuming it true, then false. In an AIC that sets the two directions of inference travel. Sudokuwiki messages use Stuart’s label, a “digit forcing chain”. That term has no added meaning, because you have to discover the almost nice loop before you identify a digit on it.

Next the Sudokuwiki path includes two *cell forcing chains*. Here is the second one. It is easy to explain in forcing chains, but impractical to find. Three forcing chains leave the candidates of r4c5 and terminate on 2r6c6. One of them must be true, so 2r6c6 must be false.

For your own experience with the impracticality of this, start at the top and send forcing chains out from every candidate of cells having three candidates. Similarly impractical is Stuart’s *unit forcing chains* sending forcing chains out from every candidate of the same value in a line. The solver also includes the special case for a four candidate unit forcing chain, the “quad forcing chain”, as a solving option.

The review post follows Sudokuwiki all the way, seeing many interesting variations, including Sudokuwiki’s simplified coloring.

In the next post of 9/17/13, we return to the grid at the first cell forcing chain to see if we can finish off Insane 475 without them, and find no suitable pink olive restrictions on 3, 4 and 5 panels. This affords an opportunity to demonstrate another type of trial in the Sysudoku repertoire, the Single Alternate Sue de Coq.

The return point grid has two SASdC examples. One is Wc1, that would be a Sue de Coq if 1r6c2 were removed. It would have a bv to match each of the alternate terms in the logical description of its contents:

4(1+2)(3+8).

It so happens that a second SASdC is available in SWc2 to remove that impediment. Its three values are described by

5(1+4)(3+5) + 835.

Why is that? The bv 14r2c2 prohibits 1 __and__ 4 in SWr2. If its 1 or 4, its also 3 or 5. The third possibility is for 1 and 4 to be missing. That would leave 835. Now if 1 or 4 is not missing, 5r9c2 has to go, because either 1 or 4 is required. And that (1+4) and the bv form a naked pair, removing the impediment 1r6c2.

So what? We put 8r7c2 and 3r8c2 and 5r8c2 on trial, winning either the solution or a very damaging set of removals, or winning the c2 removals and more removals in c1. What are they?

This is how the 835 trial turns out. Sysudoku trials are traced out in a breadth first way described on the Traces page, and diagramed with arrows to document the contradiction. See if you can follow the arrows showing how the 835 placement forces a contradiction, and what that contradiction is. Thankfully, in most cases, such diagrams are simpler, with most of the trace being bypassed by the arrows.

The enabled Sue de Coq enables an ANL confirming blue and the collapse follows.

Next is a report on the KD 485 post.

]]>As shown already from books 1 through 5, KrazyDad’s hardest, the Insane collection, is hard enough to force new ways to use familiar tools. The blog explained the nice loop in early 2012, and showed its elimination power as the AIC forms of the nice loop were encountered. But only when faced with nice loop fashioned with two ALS nodes did I realize the coloring established and given a direction by the loop could move off the loop in X-chains.

In the updated post of 8/27/13, KD Insane 465 finds a 7-wing on the last line of line marking. It’s Sysudoku practice to collect X-wings while assembling candidates. The X-wing enables a coloring cluster to be completed by basic logic. How many times have I forgotten to check for that?

After 465 gives the Insane password, a boomerang, Sudokuwiki gives up. I had an irregular XYZ wing to continue, but watchful reader Dov Mittelman had my back, and called out a faulty inference chain attaching a wing. Fortunately, there was another way to get that XYZ clue, an almost nice loop with a very unlikely ALS node supplying a slink chain terminal.

Then we come to that rare gem, a nice loop made with two ALS nodes. But the beautiful thing has no victims! When you go there and look at it, you’ll see why. The ALS node groups take up all candidates that could see adjacent nodes of the nice loop, putting them in the nodes.

So how do you make use of this beauty? By using it to introduce a new solving feature of the nice loop. An AIC can spin off the loop in two useful ways illustrated here.

A slink chain can carry the coloring out into the grid. Here a slink chain colors 4r5c6 and the C 4-group. Another connects the three 2-groups and a single 2 into a slink loop, extending the blue/green nice loop cluster to two new groups. Coloring groups is rarely useful, but it is useful to know about it.

More frequently occurring is the type of ANL extension shown here with red alternating links. If blue is true, the extension 4-chain makes 4r4c2 true, so a trial of blue can include it.

After the pink olive strikes out, the KD Insane review’s first attempt at LPO, the pattern conflict side of pattern analysis is next. A tabulation overlays pink/olive 3-candidates and the red/orange cluster candidates. The result is indecisive, and the weakened KD Insane 465 is solved with a coloring trial. It’s too easy to be fitting

The next post looks back to the update of KD 475. These updates are more than cosmetic, and back up the original solution with Sysudoku interpretations of added Sudokuwiki moves. This Insane review is particularly innovative in coloring and pattern analysis.

]]>